HIPPARCOS (an acronym for HIgh Precision PARallax COllecting Satellite) was a sc

Question

HIPPARCOS (an acronym for HIgh Precision PARallax COllecting Satellite) was a scientific mission of the European Space Agency (ESA). It was the first space experiment devoted to astrometry, the accurate measurement of star positions, distances from us, parallaxes, and proper motions.

(a) If the measured parallax shift of star A was 0.1 arcsecs and the parallax shift of star B was 0.05 arcsecs, which star was farther away from the Earth, why?
(b) What is the distance of the farthest star in parsecs?
(c) What is the distance of the farthest star in light-years?

Explanation / Answer

(a) star B is further away. Its parallax is less.   The closer a star is, the more its position changes against the background as the earth revolves around the sun. That is what parallax is.

(b) 20 parsecs. By definition, one parsec is the distance at which a star has a parallax of 1 arcsecond. Since this parallax is 1/20 as large, its distance is 20 times greater.

(c) 65.2 light years. 1 parsec = 3.26 ly, multiply that by 20.

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